Photolithography is a widely used technique for forming a desired image pattern on a substrate using light or other electromagnetic radiation. One example is the formation of integrated circuits on a semiconductor substrate. A mask imprinted with the desired pattern is used as a template for shielding the radiation according to the pattern during a photoexposure.
Two types of masks are commonly used in photolithography. One is an amplitude mask in which an image pattern is simply imprinted as opaque and transmissive features. The transmissive features have the same phase delay relative to one another. An amplitude mask can be relatively easy to manufacture but is usually limited in feature resolution and contrast.
Phase masks are another commonly used mask type in photolithography and are known for their capabilities of improving both resolution and focal depth relative to amplitude masks. Unlike amplitude masks, the features of an imprinted image pattern on a phase mask are assigned with different relative phase delays. A conventional phase mask usually operates based on the destructive interference between adjacent features with opposite phases after imaging by a finite aperture. Conventional phase masks were first proposed by Levenson et al. in IEEE Trans. Electron. Devices, Vol.29, pp. 1828, 1982 and are often referred to as "Levenson-type" phase masks.
FIG. 1a shows an amplitude mask with a simple one-dimensional two-slit pattern. Slits 110 and 120 are transmissive and the rest of the mask is opaque. The amplitude of the optical field after imaging the pattern with a finite aperture is shown in FIG. 1b. The resultant field between the two slits 110 and 120 is relatively large compared to the field transmitted through either slit and hence it can be said that the two slits are not well resolved.
Phase masks can be used in such a situation to improve the resolution using the same aperture and illumination for imaging. FIG. 2a shows a phase distribution along the x-axis of a conventional Levenson-type phase mask having two slits. The phase values of the two slit features are shifted by .pi. radians relative to each other. This leads to a destructive interference between the optical fields from the two slits in imaging and the two slits are hence better resolved. The resultant distribution of the field amplitude is shown in FIG. 2b. FIG. 2c further shows the corresponding intensity distribution in the imaging field and indicates a significant improvement in both resolution and contrast over the amplitude mask shown in FIGS. 1a and 1b.
One-dimensional images, such as the simple mask in FIG. 2a, can be assigned a phase layout with an opposite phase shift between two adjacent features. This, however, is not necessarily true for two-dimensional images. FIG. 3a illustrates an amplitude mask designed for a negative photoresist having a two-dimensional pattern with three transmissive features in opaque background. Each feature is located adjacent to the other two. If two adjacent features are assigned an opposite phase with respect to each other, two of the three neighboring features will have the same phase.
FIG. 3b shows such an example in which the grey feature is .pi.-phase shifted with respect to the other two features of the same phase. The amplitude mask of FIG. 3a suffers a severe distortion after imaging as shown in FIG. 3c. In addition, the phase mask shown in FIG. 3b cannot resolve the two features of the same phase after imaging with the same aperture and illumination (FIG. 3d). This effect is intrinsic to images of two or more dimensions in negative photoresist and is usually referred as "phase conflict". When the two adjacent features with the same phase have a phase conflict with each other, the fields from the two features constructively interfere with each other to produce a field maximum. Such undesirable interference often causes several features to merge with one another, making the images unresolvable.
Another known adverse effect associated with phase masks is spurious line formation formed by two dimensional positive photoresist masks which have transmissive background and opaque features. Conventional phase masks usually need to have transmissive features (i.e., negative photoresists) so that opposite phase values can be assigned to two adjacent features. For positive photoresists, there are no independent transmissive features which can receive the assignment of an opposite phase. One example is shown by a simple two-dimensional pattern in FIG. 4a. A mask 400 has an opaque rectangular feature 410 in the center of a transmissive background 420.
One prior-art method of forming phase masks on positive photoresisits suggests segmenting the transmissive background into different regions and applying opposite phases to adjacent regions in the background. This, however, produces undesired spurious lines at the boundaries of these features, thus resulting in adverse split of a feature. FIGS. 4b and 4c show an example of segmenting the background in the mask 400 of FIG. 4a and the resultant line formation after imaging, respectively. In FIG. 4b, the left-hand half 422 and the right-hand half 424 of the transmissive background 420 are assigned with phase delays having a phase difference of .pi.. This phase segmentation causes adverse line formation in the imaging field as shown by FIG. 4c.
Both the phase conflict in negative photoresists and line formation in positive photoresist are well recognized in the field of photolithography. Many attempts have been made to design phase masks to substantially reduce or minimize these adverse effects.
One conventional method of designing phase masks uses a pixel-by-pixel approach. This is disclosed by Liu et al. in SPIE vol. 1674, pp.14 (1992), IEEE Trans. Semiconduct. Manuf. vol.5, pp. 138 (1992) and vol.9, pp.170 (1996). This method entails finding an optimal amplitude and phase distribution over the mask using an optimization algorithm. This approach has several limitations. One limitation is the large amount of processing power that is required. The imaged pattern must be calculated for each mask variation, and these variations must be scanned over all the pixels. Therefore, the pixel-wise optimization time scales with the number of pixels to the third power (or more). Industrial masks usually have sizes of at least 10.sup.4 .times.10.sup.4 =10.sup.8 pixels. Thus, the computation times of this method can become prohibitive. Although this method has been improved to have an optimization time scaling with the number of pixels squared by using a modified algorithm which saves the scanning over pixels, it is still prohibitive for industrial-scale masks. Another limitation with this approach is that at least four levels of phase delays are usually needed for the method to be effective. This is unappealing due to the difficulty of manufacturing four-phase-level masks.
Another prior-art method in designing phase masks was disclosed by Watanabe et al. in JJAP I/12B vol.33, pp.6790 (1994). This is a multiple-exposure approach to solving the phase conflict. The method is inherently unattractive to industrial manufacturers because it takes twice the photolithography time as compared with single-exposure techniques. Another limitation of this technique is the substantial alignment and mechanical errors that often occur between the two exposures.
Pati and Kailath described a rule-based approach based on superposition of subsolutions in Journal of Optical Society of America, vol. A11, pp.2438, 1994. This method has an optimization time that scales quadratically with the number of pixels. However, the improvement introduced is in the computation time for the imaged pattern, and entails an approximation of partially coherent imaging by a fully coherent system. This is accurate only for near-fully coherent imaging due to its reliance on the linearity of field superpositions. Since many industrial lithography systems currently use either partially-coherent or fully-incoherent illumination, this approach is not widely applicable. Furthermore, the actual optimization of this method is a Gerschberg-Saxton type algorithm, which is fast but tends to settle on highly suboptimal minima. This sacrifices phase mask performance for computational speed. Finally, this approach also requires either four phase levels per mask or two-mask imaging, both of which are problematic to manufacture.
One prior-art method of adapting phase masks to positive photoresists was disclosed by Yuan et al. in JJAP I(12B) vol.33, pp. 6796 (1994). However, this method can be applied only to limited and simple cases, e.g., contact holes. In addition, this method is intended for specific phase mask technologies such as attenuated phase masks and may not work for other type of phase masks.
Cathey et al. disclosed a method for minimizing the line formation of positive-photoresist masks in U.S. Pat. Nos. 5,281,500 and 5,288,568. This method uses a "tapered" phase transition area between one phase-shifted region and an adjacent non-phase-shifted region rather than an abrupt step-like phase change shown in FIG. 4b. One disadvantage of the approach is the extreme difficulty in manufacturing a tapered mask. Another disadvantage is the need for a relatively large area to implement such tapered transition regions. This can compromise feature density and the resolution may be reduced.
Use of phase-shifting regions in negative photoresist to reduce the effect of phase conflict was described in U.S. Pat. No. 5,468,578 to Rolfson. This method uses the entire opaque region between the phase-conflicting transmissive features to become a phase-shifting transmissive region. This can lead to large negative fields printed on the photoresist, resulting in a degraded image resolution. In addition, this method only treats phase conflict between two non-phase-shifting regions. This is limiting since phase conflict also arises between adjacent phase-shifting regions. Furthermore, the computation time of this method scales quadratically with the number of pixels, which becomes impractical in designing large-scale masks for industrial use.